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Discrete & Computational Geometry

, Volume 33, Issue 2, pp 231–247 | Cite as

Cutting Triangular Cycles of Lines in Space

  • Boris AronovEmail author
  • Vladlen KoltunEmail author
  • Micha SharirEmail author
Article

Abstract

We show that n lines in 3-space can be cut into O(n2-1/69log16/69n) pieces, such that all depth cycles defined by triples of lines are eliminated. This partially resolves a long-standing open problem in computational geometry, motivated by hidden-surface removal in computer graphics.

Keywords

Computational Mathematic Open Problem Computer Graphic Computational Geometry Depth Cycle 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Copyright information

© Springer Science + Business Media Inc. 2004

Authors and Affiliations

  1. 1.Department of Computer and Information Science, Polytechnic University, Brooklyn, NY 11201-3840USA
  2. 2.Computer Science Division, University of California, Berkeley, CA 94720-1776USA
  3. 3.School of Computer Science, Tel Aviv University, Tel-Aviv 69978, Israel and Courant Institute of Mathematical Sciences, New York University, New York, NY 10012USA

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